Amichai Lampert

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20192025

most citedBias implies low rank for quartic polynomials

5 citations · 5 across the 6 of their papers we have counts for

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math.NT2025

Polynomial Bounds for Birch's Theorem

Amichai Lampert, Andrew Snowden, Tamar Ziegler

Let $K$ be a number field and $f_{1}, \dots, f_{s} \in K [x_{1}, \dots, x_{n}]$ forms of odd degrees. In 1957, Birch proved that if $n$ is sufficiently large then the forms always have a nontr…

math.NT2025

Density of solutions for systems of forms

Amichai Lampert

Let $K$ be a field of characteristic zero over which every diagonal form in sufficiently many variables admits a nontrivial solution. For example, $K$ may be a totally imaginary nu…

math.NT2024

Strength is bounded linearly by Birch rank

Benjamin Baily, Amichai Lampert

Let $f$ be a homogeneous polynomial over a field. For many fields, including number fields and function fields, we prove that the strength of $f$ is bounded above by a constant mul…

math.NT2024

Two improvements in Birch's theorem on forms

Amichai Lampert, Andrew Snowden

Let $K$ be a Birch field, that is, a field for which every diagonal form of odd degree in sufficiently many variables admits a non-zero solution; for example, $K$ could be the fiel…